Rwanda accused its much larger neighbour Uganda on Tuesday of supporting rebels opposed to the government in Kigali, a claim firmly rebutted by Kampala.

Rwandan Foreign Minister Richard Sezibera told journalists that Kigali had information that rebels of the Rwanda National Congress (RNC) "communicate with Ugandan people and give them instructions on arresting Rwandans".

"Our only concern is that the RNC is acting with and in support with people from Uganda," Sezibera said.

The RNC opposition group is made up of former Rwandan rebels who, together with Paul Kagame, are credited with stopping the 1994 genocide. The RNC was started by Kayumba Nyamwasa, a former chief of staff of the Rwandan army and once-confidant to President Paul Kagame.

But Nyamwasa fled to exile in South Africa after falling out with Kagame in 2010 and Rwanda issued an arrest warrant for him on charges of terrorism.

"We don´t see why the RNC should be part of any equation between Rwanda and Uganda. We don´t see logic of it, but for some reasons they are still operating in Uganda. And that is the awareness we raise," Sezibera insisted.

Last Thursday, Rwanda issued a travel advisory, warning its citizens against visiting Uganda as they may face illegal arrests, torture, and deportations.

This came after Rwanda claimed 986 of its citizens were deported from Uganda, and almost 200 were being held incommunicado.

Uganda rejected the claims.

"It is false that Uganda hosts any elements fighting Rwanda," Foreign Affairs Minister Sam Kutesa said in a statement.

"Uganda does not and cannot allow anyone to operate from its territory that threatens a neighbour as alleged."

Kutesa also denied that Uganda "arrests, tortures and harasses Rwandans".

People from Rwanda were welcome to visit Uganda, the minister underlined, and had nothing to fear as long as "they are law abiding".

"As a country that has been a target of terrorist attacks... we remain vigilant," said Kutesa. "In this regard, the government of Uganda remains committed to protecting the security of its citizens and its borders and will act accordingly against local or foreign threats."

He said it was "unfortunate" that the movement of goods and people across the common border has been affected by the row.

The scuffle between Rwanda and Uganda threatens the six-member East African Community, a regional economic bloc.

Both countries were involved in the so-called Great War of Africa which began in Democratic Republic of Congo in 1998 and drew in most of the region.

Rwanda and Uganda are both led by former rebel leaders now ruling beyond their initial two-term limits after changing the respective constitutions.

Yoweri Mueveni of Uganda has been in power since 1986 while Paul Kagame has ruled Rwanda since 2000 and is now serving a seven-year third term that will conclude in 2021.